In a C++ Linux app, what is the simplest way to get the functionality that the Interlocked functions on Win32 provide? Specifically, a lightweight way to atomically increment or add 32 or 64 bit integers?

Strictly speaking, Linux cannot offer atomic "interlocked" functions like ones in Win32, simply because these functions require hardware support, and Linux runs on some platforms that don't offer that support. Having said that, if you can constrain yourself to Intel x68/x64, take a look at the implementation of reference counting in Boost shared pointers library.

The fairly common glib library that's used in GTK and QT programming as well as standalone offers a variety of atomic operations. See http://library.gnome.org/devel/glib/2.16/glib-Atomic-Operations.html for a list. There are g_atomic functions for most of the operations that Interlocked supports on Win32, and on platforms where the hardware directly supports these, they are inlined as the needed assembly code.